For years petrophysicists interpreted logs as if all formations were locally homogenous and isotropic. They did this even though they well understood that sedimentary deposition occurs layer by layer, making transversely isotropic, TI, media the rule rather than the exception in sedimentary geology. With the widespread availability of multi-component induction logging technology petrophysicists are more willing to use TI resistivity models (i.e., R h and R v ). Generally, sediments buried a few hundred meters or more are subject to a principal stress aligned with the overburden. In many environments, depending on mechanical properties, this leads to bedding perpendicular fractures, which can give rise to biaxial anisotropy in the macroscopic petrophysical properties.We have developed resistivity models for laminated sand-sale formations in the presence of drilling-induced and natural fractures. The principal resistivities R x , R y , R z are expressed as a function of horizontal and vertical resistivities of unfractured formation, fracture porosity and resistivity of fracture which is the resistivity of mud filtrate in the case of drilling induced fractures or the connate water resistivity and saturation in the case of natural fractures. These models allowed us to study the effect of fractures on the three principal resistivities as a function of laminated shale content and as a function of fracture porosity for both drilling induced and natural fractures. The combined three-step analysis of measured principal resistivities based on the modular concept allows a separation and quantification of the two anisotropy sources: fracturing and lamination. The analysis based on the three principal resistivities provides an estimate of fracture porosity, resistivity of the porous sand fraction (without fractures) and water saturations. We have also developed an inversion algorithm for the biaxially anisotropic formations that reliably determines three principal resistivities from multi-component induction measurements. First, in the least-square inversion the multi-frequency focused magnetic field tensor is rotated to the principal coordinate system. This rotation is characterized by three angles: ϕ, θ, and ψ; and three principal, diagonal magnetic field components H xx , H yy , and H zz . After the three angles and three principal components are determined, we recover principal formation resistivities using a fast inversion algorithm based on a look-up table approach. To validate the theory and algorithms described above, we have simulated the multi-component induction measurements in thick biaxially anisotropic layers for various sets of parameters and used the software to process the data. The new approach was also applied to the real measurements acquired in the well with drilling induced fractures and as a result principal formation resistivities, fracture orientation, and fracture porosity were reliably determined.
New induction logging hardware makes it possible to obtain both resistivity and resistivity anisotropy data. Resistivity anisotropy, the ratio of vertical to horizontal resistivity is the macroscopic effect of thinly layered formations in which logging tools have insufficient vertical resolution to properly resolve the individual beds or laminae. Generally, there are two types of layering:Laminated shaly sands. The sediment consists of thin bedded sand-shale sequences (anisotropy in these sands originates from the contrast of shale and sand resistivity).Finely layered anisotropic sands. The sand is composed of layers of different grain sizes and/or sorting (anisotropy in these sands originates from the resistivity contrast associated with the different water saturation). The interpretation of conventional resistivity data is well understood. However, interpretation of vertical resistivity and resistivity anisotropy is not well understood and often counterintuitive. We have used forward modeling to illustrate the effects of porosity variability in layered formations. For example, we have investigated the porosity layering effect, which varies from an average porosity of 20 p.u. by +/–5, 10, 15 p.u.. Three types of layering were considered: graded bedding, square- and sin2-variation of porosity with depth. The modeling shows that sharp bed boundaries create the maximum resistivity anisotropy for any two component resistivity distributions. The new induction logging hardware is comprised of three mutually orthogonal transmitter-receiver coil configurations measuring all necessary data to derive both resistivity and resistivity anisotropy of the formation in vertical, deviated, and horizontal wells. Simple models illustrate the physics and the tools' capabilities are demonstrated with a synthetic example. Based on the petrophysical analysis of porosity contrast and layering type, a resistivity model is constructed and the tool responses of this model are computed. Using state-of-the-art inversion techniques, both resistivity and resistivity anisotropy can be recovered. Introduction Evaluation of thinly laminated reservoirs is critical in today's deepwater plays. In most deep water plays (i.e., Gulf of Mexico, west of Africa, offshore Brazil), thinly laminated turbidite sands are associated with large hydrocarbon accumulations. Because deepwater development costs are high, it is essential that the reserves be accurately determined. However, these sand packages are both difficult to identify and accurately evaluate with conventional co-axial induction tool data. Newly developed multicomponent induction hardware facilitates the accurate evaluation of such thinly laminated sand-shale sequences. Further, recognition of the presence of thin, clean sand lamina is important because laminated sands are much more productive than uniform, dispersed shaly-sands. Generally, when a potential reservoir containing thinly laminated sands and shales is recognized, petrophysicists and log analysts correct the low resistivity induction log data for thin bed effects. Once corrected they then calculate saturations and compute reserves based on one of the many shaly-sand evaluation equations1,2. However, even then it is not uncommon to underestimate the hydrocarbon volume and bypass pay. Klein3–5recognized that conventional induction log resistivity underestimated the resistivity of thin sand components in a laminated sand-shale sequence. Even though the thin, individual sand and shale lamina may be isotropic, the layered sequence of sands and shales appear anisotropic on the scale of the logging tool measurements. Klein4, and Klein et al.6,7, and Hagiwara8–10derived simple averaging expressions for the macroscopic vertical and horizontal resistivities.
This paper was prepared for presentation at the 1999 SPE Annual Technical Conference and Exhibition held in Houston, Texas, 3–6 October 1999.
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